It seems to be the fate of Conservative prime ministers to be stalked by flamboyantly ambitious blonds with connections to Henley, wild hair and untamed rhetoric. In the case of Margaret Thatcher, it was Michael Heseltine, her nemesis but not her successor. For David Cameron, the predator is Boris Johnson, who pulsates with the urge to be both.

At this week's Conservative conference in Birmingham, the official target will be Ed Miliband and the audacious land grab that he launched in Manchester for the title of "One Nation" party. The real enemy, the person whose name most makes the prime minister's people twitch, will be Boris Johnson. As our poll today underscores, he leads overwhelmingly on what was once considered to be David Cameron's greatest gift: being able to attract voters who might not normally support the Conservative party.

The prime minister's aides insist that relations between the two old Etonians are fine, though if they were really that tickety-boo they would not have needed to stage a "reconciliation" meeting before the conference. Mr Cameron's friends also say that he and they are entirely relaxed about Boris basking in the conference sun. Sure they are: as relaxed as they were about the mayor comprehensively upstaging the prime minister during the Olympics, as relaxed as a cat on a hot tin roof.

Those of them who do admit that Boris is a problem say that at least: "There are worse rivals you could have." There's some truth in that. The mayor is not a member of the cabinet. Being detached from the government, and all the unpopular and misconceived decisions that it has made, is part of the explanation for why he is much the most popular Tory politician. To be prime minister, however, it is usually thought essential to be a member of cabinet. He is not even a member of the Commons, though if he decided to seek a seat through a byelection, with the Heathrow issue as a ready-made cause/excuse, there is more than one Conservative MP ready to step down for him. But for Mr Cameron's allies to find consolation from the mayor being in no current position to strike is to miss an essential point. The threat is not of a leadership challenge any time soon. The mayor casts a shadow over the prime minister because he allows the Conservative party to imagine how things could be different with someone else in charge. The dream might well be a delusion, but it is nevertheless a seductive fantasy for a growing number of Tories. Boris is a walking, wisecracking reminder to them and to David Cameron of what the Tory leader has lost since he moved into Number 10.

One is an ability to excite the Tory party. It is important to note that this has only a little bit to do with any policy differences between them. Boris has used Europe as a dividing line with the man he would replace. While the prime minister havers about whether to promise a referendum on Europe and feels obliged to advocate the salvation of the euro, the mayor, unburdened by any responsibility to think too deeply about the consequences, demands a plebiscite and wishes death to the euro, a position naturally more popular with Europhobic Tories. Other than Europe, you really have to look very hard to locate meaningful differences between two Tories of similar age whose formative political years were dominated by Margaret Thatcher. The budget cut in the top rate of tax, the biggest strategic error in terms of how the public views the Tories and one that Labour returned to over and again at their conference, had been demanded in advance by the mayor. Indeed, he had argued for going even further and abolishing the top rate altogether.

Boris is as much, if not more so, a liberal on social issues as his rival in Number 10. He has spoken up for being generous about immigration and wore a pink stetson at a gay pride march, which makes his popularity among some of the unreconstructed right of the Tory party rather bewildering. But, then, it is a mistake to think of the Boris phenomenon in rational terms. His appeal is not founded on policy, but on his ability to stimulate the erogenous zones of Tories. One of the easiest predictions that we can make about this conference is that Boris will attract larger crowds and receive from them a more fervent reception than any member of the cabinet. We will see the evidence of that at a rally for him on Monday night staged by ConservativeHome and entitled "Boris's 2012: Re-elected and Olympotastic". Says one of his friends: "That will be where you see Boris unleashed." Since he is never exactly leashed at any time that should be interesting.

The following morning, he will address the conference itself, a glorious opportunity for Borisovian grandstanding and an event that the prime minister will feel painfully obliged to attend. The compliment will not be returned: the mayor will have left Birmingham before Mr Cameron addresses the party. Cabinet ministers have to clear their conference speeches through Number 10. The prime minister's people would very much like to see what Mr Johnson has in store for the conference. One Number 10 aide says: "He's talked to us about where his speech is going." In other words, they don't really have a clue. If it is comedy Boris, he will make the rest of the cabinet look even more cardboard and grey. If it is serious Boris, the would-be prime minister in waiting, that will be really alarming for Number 10.

The most important thing that Boris has which the prime minister lacks is popularity. No Tory needs reminding that David Cameron failed to achieve a clean victory at the supposedly unlosable election of 2010 and growing numbers of the nervous and fractious blue clan are expressing fears that their party will do no better, and could well do much worse, in 2015. By contrast, Boris is the only Tory to have won a major election since 1992, and he has done so twice in London, a naturally non-Tory city.

Put simply, Dave looks like a loser, Boris looks like a winner. The Tory tribe is drawn to risk-takers, characters and winners, especially winners – and Boris is all three. He is the only politician in the land known by his first name; during the Olympics, he had a crowd of 60,000 chanting it. "Boris! Boris! Boris!" they cried. Can anyone recall any other Tory – or indeed any politician of any party – who can draw that response from a non-partisan audience?

He has a talent for cheering up people, a very useful quality in the middle of a double-dip recession. Owning optimism is always a hugely valuable asset for politicians and even more so when times are tough. Nick Clegg tried for it in Brighton when he sought to persuade his party that things would come right for them in the end. Ed Miliband strove for it in Manchester with his projection of himself as the man who could bring Britain back together. David Cameron used to own optimism when he was leader of the opposition and will try to recapture it in his conference speech. Boris already has it.

Allied with that is the feeling that he is "authentic" in a way other politicians are not. To adapt Oscar Wilde, authenticity is everything in politics – once you can fake that, you are made. It is also important to note that being regarded as authentic should not be confused with being truthful. Boris has had a very on-off relationship with the truth over the years. It is striking that those who know him best often trust him least and his career is littered with incident, political and personal, which would have felled most other politicians long ago. His ability to be unscathed by scandal is another thing that he has and which his rival at Number 10 used to possess, but has now lost: a Teflon quality that means nothing ever really sticks.

All this may change. For Cameron loyalists, Boris is a firework that will soon splutter out as Olympic euphoria fades and people start to ask serious questions about his fitness for the highest office. They have a point. There is a vast difference between being mayor of London, a glorified transport and police commissioner, and having your finger hovering over the nuclear button. Borismania may prove to be a passing spasm, which evaporates just as Cleggmania did.

He is currently hailed by rightwingers as being a truer Tory than David Cameron while also being more popular among non-Tories, a contradiction that will be hard to sustain forever. Between City Hall and Number 10, there are a huge number of high hurdles to leap. Being the front runner for a leadership succession has historically proved to be a long-term disadvantage. In a contest for the Tory crown, the darker sides of Boris would come under a lot more scrutiny than they do now, not least because his rivals will be sure to get them out there.

Will Boris make an overt move to supplant David Cameron? That I doubt at the moment. He does not have to be actively plotting to undermine the prime minister. To hurt David Cameron, Boris just has to be Boris. And at that, as we know, he is terribly good.